Abstract:
Approximate recurrence relations (RR) in the three-dimensional Ising model are obtained in the form of rapidly convergent series. The representation of RR in the form of nonasymptotical series is related to rejecting the traditional perturbation theory based on the Gaussian measure density. Using the RR obtained, value of the critical exponent of the correlation length ν is calculated. It is shown that if higher nongaussian basic measures are used then the difference form of the RR implies independence of the critical exponent ν of s for s>2 (s is the parameter of the layer structure of the phase space). The results obtained make it possible to obtain explicit expressions for thermodynamic functions in the neighbourhood of the phase transition point.
Citation:
M. P. Kozlovskii, “Nonasymptotic form of the recursion relations of the three-dimensional Ising model”, TMF, 78:3 (1989), 422–433; Theoret. and Math. Phys., 78:3 (1989), 300–308
This publication is cited in the following 13 articles:
Yukhnovskii I.R., Kozlovskii M.P., Pylyuk I.V., “Critical Behavior of a 3D Ising-Like System in the Higher Non-Gaussian Approximation: Inclusion of the Critical Exponent of the Correlation Function”, Int. J. Mod. Phys. B, 28:24 (2014), 1450160
Pylyuk I.V., Ulyak M.V., “Critical Behaviour of a 3D Ising-Like System in the Rho(6) Model Approximation: Role of the Correction for the Potential Averaging”, Condens. Matter Phys., 15:4 (2012)
Pylyuk I.V., Kozlovskii M.P., “Calculation of free energy of a three-dimensional Ising-like system in an external field with the use of the rho(6) model”, Physica a-Statistical Mechanics and its Applications, 389:23 (2010), 5390–5401
Yukhnovskii, IR, “Study of the critical behaviour of three-dimensional Ising-like systems on the basis of the rho(6) model with allowance for microscopic parameters: II. Low-temperature region”, Journal of Physics-Condensed Matter, 14:45 (2002), 11701
Yukhnovskii, IR, “Study of the critical behaviour of three-dimensional Ising-like systems on the basis of the rho(6) model with allowance for microscopic parameters: I. High-temperature region”, Journal of Physics-Condensed Matter, 14:43 (2002), 10113
Yukhnovskii, IR, “Thermodynamics of three-dimensional Ising-like systems in the higher non-Gaussian approximation: Calculational method and dependence on microscopic parameters”, Physical Review B, 66:13 (2002), 134410
Pylyuk, IV, “Description of critical behavior of Ising ferromagnet in the rho(6) model approximation taking into account confluent correction. I. Region above the phase transition point”, Low Temperature Physics, 25:11 (1999), 877
I. V. Pylyuk, “Critical behavior of the three-dimensional Ising sistem: Dependence of themodynamic characteristics on microscopic parameters”, Theoret. and Math. Phys., 117:3 (1998), 1459–1482
M.P. Kozlovskii, I.V. Pylyuk, V.V. Dukhovii, “Equation of state of the 3D Ising model with an exponentially decreasing potential in the external field”, Journal of Magnetism and Magnetic Materials, 169:3 (1997), 335
V. V. Dukhovyi, M. P. Kozlovskii, I. V. Pylyuk, “Equation of state in 3-D Ising model from microscopic level calculation”, Theoret. and Math. Phys., 107:2 (1996), 650–666
M. P. Kozlovskii, I. V. Pylyuk, Z. E. Usatenko, “Method of calculating the critical temperature of three‐dimensional Ising‐like system using the non‐gaussian distribution”, Physica Status Solidi (b), 197:2 (1996), 465
M. P. Kozlovskii, I. V. Pylyuk, “Entropy and specific heat of the 3D ising model as functions of temperature and microscopic parameters of the system”, Physica Status Solidi (b), 183:1 (1994), 243
M. P. Kozlovskii, I. V. Pylyuk, I. R. Yukhnovskii, “Thermodynamic functions of three-dimensional ising model near the phase transition point with allowance for corrections to scaling. I. The case T>Tc”, Theoret. and Math. Phys., 87:2 (1991), 540–556
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